Robust constrained model predictive control using contraction theory

This paper presents a novel robust constrained model predictive control (MPC) method that exploits the contracting dynamics of a nonlinear system. The proposed technique can be applied to a class of nonlinear systems whose dynamics are contracting in a tube centered around the nominal state trajectory predicted at time t₀. Compared to robust MPC strategies based on Lipschitz continuity, the method employed here: 1) can tolerate larger disturbances; and 2) is feasible for a larger prediction horizon and could enlarge the feasible region accordingly. The paper explicitly evaluates the maximum disturbance that can be tolerated by the proposed control strategy. It also derives sufficient conditions for the recursive feasibility of the optimization problem and for the practical asymptotic stability of the closed-loop system. A simulation example illustrates the effectiveness of the proposed method.